tl;dr discover bug, write test that fails because of the bug, fix bug, don't worry about it again
If you're not sure how to get started or if you're looking for a way to ease into testing, antifragility testing is a great. Antifragility is based on the idea that some things get stronger when subjected to shock. As your application grows, bugs will pop up here and there, and you'll be tasked to fix them.
However, before fixing the bug, you can write a test that fails because of the bug. For instance, if you have a form that creates a user and isn't validating the username properly, you can write a test that specifically checks validation for that field. You might call the test username_validation_should_fail_when_length_is_less_than_8. It may seem comical to have such a long name (and perhaps you could shorten it), but it's important to write very specific tests. You could then test validation by passing in values that you know should fail. Before fixing the bug, you can run the test and cause the test to fail. Then after fixing the bug, you can be confident that it won't fail again.
In this way, bugs are still a nuisance, but at least they will make your application stronger over time. After all, you should never have to fix the same bug twice.